Seminars and Colloquia by Series

TBA by Fan Wei

Series
Graph Theory Seminar
Time
Tuesday, May 4, 2021 - 15:45 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Fan WeiPrinceton University

TBA

Global Constraints within the Developmental Program of the Drosophila Wing

Series
Mathematical Biology Seminar
Time
Friday, April 30, 2021 - 15:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Madhav ManiNorthwestern University

Organismal development is a complex process, involving a vast number of molecular constituents interacting on multiple spatio-temporal scales in the formation of intricate body structures. Despite this complexity, development is remarkably reproducible and displays tolerance to both genetic and environmental perturbations. This robustness implies the existence of hidden simplicities in developmental programs. Here, using the Drosophila wing as a model system, we develop a new quantitative strategy that enables a robust description of biologically salient phenotypic variation. Analyzing natural phenotypic variation across a highly outbred population, and variation generated by weak perturbations in genetic and environmental conditions, we observe a highly constrained set of wing phenotypes. Remarkably, the phenotypic variants can be described by a single integrated mode that corresponds to a non-intuitive combination of structural variations across the wing. This work demonstrates the presence of constraints that funnel environmental inputs and genetic variation into phenotypes stretched along a single axis in morphological space. Our results provide quantitative insights into the nature of robustness in complex forms while yet accommodating the potential for evolutionary variations. Methodologically, we introduce a general strategy for finding such invariances in other developmental contexts. -- https://www.biorxiv.org/content/10.1101/2020.10.13.333740v3

Meeting Link: https://gatech.bluejeans.com/348270750

TBA by Bernard Lidický

Series
Graph Theory Seminar
Time
Tuesday, April 27, 2021 - 15:45 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Bernard LidickýIowa State University

TBA

On Scalable and Fast Langevin-Dynamics-Based Sampling Algorithms

Series
Dissertation Defense
Time
Friday, April 23, 2021 - 15:00 for 1.5 hours (actually 80 minutes)
Location
ONLINE
Speaker
Ruilin LiGeorgia Institute of Technology

Please Note: Meeting link: https://bluejeans.com/7708995345

Langevin dynamics-based sampling algorithms are arguably among the most widely-used Markov Chain Monte Carlo (MCMC) methods. Two main directions of the modern study of MCMC methods are (i) How to scale MCMC methods to big data applications, and (ii) Tight convergence analysis of MCMC algorithms, with explicit dependence on various characteristics of the target distribution, in a non-asymptotic manner.

This thesis continues the previous efforts in these two lines and consists of three parts. In the first part, we study stochastic gradient MCMC methods for large-scale applications. We propose a non-uniform subsampling of gradients scheme to approximately match the transition kernel of a base MCMC base with full gradient, aiming for better sample quality. The demonstration is based on underdamped Langevin dynamics.

In the second part, we consider an analog of Nesterov's accelerated algorithm in optimization for sampling. We derive a  dynamics termed Hessian-Free-High-Resolution (HFHR) dynamics, from a high-resolution ordinary differential equation description of Nesterov's accelerated algorithm. We then quantify the acceleration of HFHR over underdamped Langevin dynamics at both continuous dynamics level and discrete algorithm level.

In the third part, we study a broad family of bounded, contractive-SDE-based sampling algorithms via mean-square analysis. We show how to extend the applicability of classical mean-square analysis from finite time to infinite time. Iteration complexity in the 2-Wasserstein distance is also characterized and when applied to the Langevin Monte Carlo algorithm, we obtain an improved iteration complexity bound.

Learning Gaussian mixtures with algebraic structure

Series
Stochastics Seminar
Time
Thursday, April 22, 2021 - 15:30 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/129119189
Speaker
Victor-Emmanuel BrunelENSAE/CREST

We will consider a model of mixtures of Gaussian distributions, called Multi-Reference Alignment, which has been motivated by imaging techniques in chemistry. In that model, the centers are all related with each other by the action of a (known) group of isometries. In other words, each observation is a noisy version of an isometric transformation of some fixed vector, where the isometric transformation is taken at random from some group of isometries and is not observed. Our goal is to learn that fixed vector, whose orbit by the action of the group determines the set of centers of the mixture. First, we will discuss the asymptotic performances of the maximum-likelihood estimator, exhibiting two scenarios that yield different rates. We will then move on to a non-asymptotic, minimax approach of the problem.

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